This paper investigates the variability of the risk premium in the Spanish stock market over the period 1970-90. A first approach analizes the relationship between expected excess stock returns and volatility using an ARIMA model in the regressor variable. An exploratory study, using non-parametric methods, suggests the possibility of using a GARCH-M model, which is attractive because it generates a natural measure of risk. Empirical analysis shows a clearly significant persistence of volatility of stock prices in the whole sample period. This is consistent with the recent theories on assetpricing models. The results oblained indicate that the risk assumed by the spanish investor has been sufficiently compensated. Moreover, in some periods, the efficient market hypothesis can not be accepted.